Joseph McCann, 34, is accused of 37 charges including multiple rapes, kidnap and false imprisonment involving 11 victims, one as young as 11 years old, over three days in April and May.
Opening his Old Bailey trial, John Price QC told how one of the alleged victims, a 25-year-old woman, was snatched as she walked home in Walthamstow, east London, just after midnight on April 25.
Mr Price told jurors: "He told her to stop screaming or he would stab her.
"He dragged her to a nearby car, pushed her inside and drove off."
The prosecutor said the woman was raped "many times" over the next 14 hours and subjected to acts of "shocking depravity and violence".
Mr Price went on: "He hit her and threatened to smash a vodka bottle in her face.
"Very many sexual assaults upon her took place in various locations, in and out of the car.
"He made her call him 'daddy' and say that she was a child.
"At one point the man parked the car near to a school, saying that he wanted to make her rape a child. He raped (the woman) at that location.
"On occasions he said he would put her in the canal to wash his DNA off her.
"At other times he said he would take her away to Europe and never release her."
Just after midday on the same day, McCann allegedly abducted a 21-year-old woman in Edgware, north London, while still holding prisoner his first alleged victim.
Jurors were shown CCTV footage of the alleged abduction.
The victim is seen being bundled into a silver Ford S Max car while her younger sister manages to get away and run home screaming.
The younger sibling could be heard weeping as her mother explained what happened in a 999 call.
The two women managed to escape in Watford after the 25-year-old hit McCann over the head with a vodka bottle, jurors heard.
Mr Price said they were not the first victims, the defendant having struck in Watford a couple of days before on Sunday, April 21.
A 21-year-old woman was snatched at knifepoint as she walked from a nightclub called Pryzm, the court heard.
Mr Price told how McCann allegedly continued his spree of sex attacks in the North West 10 days later.
Over 12 hours on May 5, he allegedly attacked three women, three young girls and a boy of 11.
He allegedly conned his way into a mother's Greater Manchester home, tied her to a bed and raped her 17-year-old daughter and 11-year-old son.
Afterwards, he allegedly abducted a 71-year-old woman in her own Fiat car at a Morrison's car park.
He raped the pensioner and went on to kidnap and sexually assault a 13-year-old girl before both managed to escape at Knutsford Service Station on the M6, the court heard.
McCann made off in the Fiat, which he used to snatch two 14-year-old girls in Cheshire, it was alleged.
Not guilty pleas have been entered on all the charges relating to the 11 alleged victims.
McCann, of Harrow, north west London, is charged with 10 counts of false imprisonment, seven counts of rape, one count of rape of a child, two counts of causing or inciting a person to engage in sexual activity without consent, seven counts of kidnap, one count of attempted kidnap, three counts of causing or inciting a child under 13 to engage in sexual activity, three counts of assault by penetration, one count of sexual assault and two counts of committing a sexual offence with intent.
McCann was not in the dock of the Old Bailey as Mr Price outlined the prosecution case to jurors.
The trial, which is due to go on for six weeks, was adjourned until Wednesday morning.